Neural dynamical systems with stable attractor structures, such as point
attractors and continuous attractors, are hypothesized to underlie meaningful
temporal behavior that requires working memory. However, working memory may not
support useful learning signals necessary to adapt to changes in the temporal
structure of the environment. We show that in addition to the continuous
attractors that are widely implicated, periodic and quasi-periodic attractors
can also support learning arbitrarily long temporal relationships. Unlike the
continuous attractors that suffer from the fine-tuning problem, the less
explored quasi-periodic attractors are uniquely qualified for learning to
produce temporally structured behavior. Our theory has broad implications for
the design of artificial learning systems and makes predictions about
observable signatures of biological neural dynamics that can support temporal
dependence learning and working memory. Based on our theory, we developed a new
initialization scheme for artificial recurrent neural networks that outperforms
standard methods for tasks that require learning temporal dynamics. Moreover,
we propose a robust recurrent memory mechanism for integrating and maintaining
head direction without a ring attractor.

基于我们的理论，我们为人工循环神经网络开发了一种新的初始化方案，优于需要学习时间动态的标准方法，并且提出了一种稳健的循环记忆机制，用于集成和维持方向信息而不需要环形吸引子。

无需连续吸引子的持续学习信号和工作记忆

Persistent learning signals and working memory without continuous  attractors

In motor neuroscience, artificial recurrent neural networks models often
complement animal studies. However, most modeling efforts are limited to
data-fitting, and the few that examine virtual embodied agents in a
reinforcement learning context, do not draw direct comparisons to their
biological counterparts. Our study addressing this gap, by uncovering
structured neural activity of a virtual robot performing legged locomotion that
directly support experimental findings of primate walking and cycling. We find
that embodied agents trained to walk exhibit smooth dynamics that avoid
tangling -- or opposing neural trajectories in neighboring neural space -- a
core principle in computational neuroscience. Specifically, across a wide suite
of gaits, the agent displays neural trajectories in the recurrent layers are
less tangled than those in the input-driven actuation layers. To better
interpret the neural separation of these elliptical-shaped trajectories, we
identify speed axes that maximizes variance of mean activity across different
forward, lateral, and rotational speed conditions.

通过研究虚拟机器人在进行腿部运动时的结构化神经活动，我们发现机器人训练后的神经轨迹比输入驱动的激励层的神经轨迹更为复杂，这一核心原则对于计算神经科学具有重要意义。

从数据拟合到探索：通过强化学习解读运动控制的神经动力学

From Data-Fitting to Discovery: Interpreting the Neural Dynamics of  Motor Control through Reinforcement Learning

We show that the mutual information between two symbols, as a function of the
number of symbols between the two, decays exponentially in any probabilistic
regular grammar, but can decay like a power law for a context-free grammar.
This result about formal languages is closely related to a well-known result in
classical statistical mechanics that there are no phase transitions in
dimensions fewer than two. It is also related to the emergence of power-law
correlations in turbulence and cosmological inflation through recursive
generative processes. We elucidate these physics connections and comment on
potential applications of our results to machine learning tasks like training
artificial recurrent neural networks. Along the way, we introduce a useful
quantity which we dub the rational mutual information and discuss
generalizations of our claims involving more complicated Bayesian networks.

该研究论文阐述了对于正则文法的符号间互信息随符号间距离指数衰减的特性，然而对于上下文无关文法则符合幂律分布；并且将该现象与统计力学、湍流以及宇宙膨胀等领域的幂律相关性做了联系，以及阐述了这种现象在机器学习中的潜在应用。除此之外，该研究论文还提出了一种合理的互信息量的量化方式，并探讨了该现象在更复杂的贝叶斯网络中的推广。